Faster and simpler online/sliding rightmost Lempel-Ziv factorizations
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866911979682136064 |
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| author | Sumiyoshi, Wataru Mieno, Takuya Inenaga, Shunsuke |
| author_facet | Sumiyoshi, Wataru Mieno, Takuya Inenaga, Shunsuke |
| contents | We tackle the problems of computing the rightmost variant of the Lempel-Ziv factorizations in the online/sliding model. Previous best bounds for this problem are O(n log n) time with O(n) space, due to Amir et al. [IPL 2002] for the online model, and due to Larsson [CPM 2014] for the sliding model. In this paper, we present faster O(n log n/log log n)-time solutions to both of the online/sliding models. Our algorithms are built on a simple data structure named BP-linked trees, and on a slightly improved version of the range minimum/maximum query (RmQ/RMQ) data structure on a dynamic list of integers. We also present other applications of our algorithms. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_03008 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Faster and simpler online/sliding rightmost Lempel-Ziv factorizations Sumiyoshi, Wataru Mieno, Takuya Inenaga, Shunsuke Data Structures and Algorithms We tackle the problems of computing the rightmost variant of the Lempel-Ziv factorizations in the online/sliding model. Previous best bounds for this problem are O(n log n) time with O(n) space, due to Amir et al. [IPL 2002] for the online model, and due to Larsson [CPM 2014] for the sliding model. In this paper, we present faster O(n log n/log log n)-time solutions to both of the online/sliding models. Our algorithms are built on a simple data structure named BP-linked trees, and on a slightly improved version of the range minimum/maximum query (RmQ/RMQ) data structure on a dynamic list of integers. We also present other applications of our algorithms. |
| title | Faster and simpler online/sliding rightmost Lempel-Ziv factorizations |
| topic | Data Structures and Algorithms |
| url | https://arxiv.org/abs/2408.03008 |